Answer
$-2$ is a solution.
Work Step by Step
Let's note
$f(x)=2x^3-3x^2-11x+6$.
We have $f(c)=0$ if the remainder of the division of $f(x)$ by $x-c$ is $0$.
The value of $c$ is $-2$.
Use synthetic division
$\begin{matrix}
-2) &2&-3&-11&6 \\
& &-4&14&-6 \\
& --&--&--& --\\
& 2&-7&3&0
\end{matrix}$
The remainder is zero, therefore $f(-2)=0$, which means $-2$ is a solution of the equation $f(x)=0$.
